∞ Calculus II

1st and 2nd order ODEs, calculus on curves, differential calculus in Rⁿ, vector functions, multiple integrals, vector fields, Fourier series and transforms. Every topic with step-by-step theory, worked examples and solved exercises.

📋 Formulario

Complete Theory

Worked Examples

Example 1ODE with complex roots
Example 2Particular solution (undetermined coefficients)
Example 3Variation of parameters
Example 4Resonance
Example 5Classifying a 2×2 system equilibrium

Exercises with Solutions

Exercise 1HomogeneousMedium
📋 Problem to solve
Solve y′′−3y′+2y=0y''-3y'+2y=0.
Exercise 2HomogeneousMedium
📋 Problem to solve
Solve y′′+2y′+5y=0y''+2y'+5y=0.
Exercise 3Variation of parametersHard
📋 Problem to solve
Solve y′′−y=exy''-y=e^x via variation of parameters.
Exercise 4SystemsHard
📋 Problem to solve
Classify the equilibrium of x′=x+yx'=x+y, y′=4x+yy'=4x+y.
Exercise 5ResonanceMedium
📋 Problem to solve
Solve y′′+y=cos⁡xy''+y=\cos x, y(0)=0y(0)=0, y′(0)=1y'(0)=1.
Exercise 6Critical dampingMedium
📋 Problem to solve
Solve y′′+4y′+4y=0y''+4y'+4y=0 and state the damping type.
Exercise 7SystemsHard
📋 Problem to solve
Classify the equilibrium of x′=(0−110)x\mathbf{x}'=\begin{pmatrix}0&-1\\1&0\end{pmatrix}\mathbf{x}.
📚

Recommended Books

Introductory
Calculus: Early Transcendentals
Stewart, Clegg, Watson
Buy on Amazon →
Intermediate
Multivariable Calculus
Stewart, Watson, Clegg
Buy on Amazon →

As an Amazon Associate I earn from qualifying purchases.